Chern-Simons-matter theories at large baryon number

We study SU(2) Chern-Simons theories at level k coupled to a scalar on T-2 x Double-struck capital R at large baryon number. We find a homogeneous but anisotropic ground state configuration for any values of k on the IR fixed-point of those models. This classical analysis is valid as long as we take the baryon number large. As a corollary, by comparing the symmetry breaking pattern at large chemical potential, we find that the theory does not reduce to the singlet sector of the O(4) Wilson-Fisher fixed-point at large-k, as expected from general grounds. This paper will be one primitive step towards quantitative analysis of Chern-Simons-matter dualities using the large charge expansion.